Observing the outcome of a very large number N of trials, we pick out all the trial that include . The number of those chosen trials will be : N*[1-0.75^7].

We now remove only one Y hat from each of the chosen outcomes, which leaves us with the above found number of outcomes which have now only 6 hats in each group.

The number of cases (out of the chosen group) which include at least one B hat, will be : N*[1-0.75^7]*[1-0.75^6] .

Out of this new group we remove now one B hat from each outcome, and continue in the same fashion with the remaining two colors, bringing us to a remaining group of outcomes that originally contained at least one of each color. So the probability of having all 4 colors in a trial will be :